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special thanks to Katrina EG for posting
this amazing geometry question on X the
end result is literally going to shock
you we have this big semicircle and
inside it we have two small semicircles
of diameter two and three and this
yellow one is tangent to the red
semicircle our job is to find the
diameter of the big
semicircle so can you solve it at first
glance if we pull this down here it
looks like the bigger diameter is simply
the sum of both of these diameters so
the answer we are looking for is five or
it will be approximately five but now
how to find out the exact value of this
diameter for that we will break this
diameter into smaller sections this this
and this one this piece right here is
the same as the radius of this
semicircle and thus it will be of length
one now to find the length of this part
first draw this radius and then join
both of these radi together this will be
1.5 and this will be 1 + 1.5 or
2.5 now we will use Pythagoras Theorem
to find the length of this part we can
do the math to find it and I have done
it for you in case you might want to
check but we have an easier method to
figure it out if we multiply the length
of both of these sides by two we get the
this as three and this is five and thus
we know that it is a three four five
Pythagorean triplets and therefore this
will be four or if we divide it by two
we get this side length as two excellent
next we will find the length of this
part and we are done let us label this
as y now here comes the magic this is
what I found the most intelligent way to
solve for this part complete this circle
now make a rectangle around it so the
length of this side of the rectangle
will be the same as the diameter of this
circle which will be three now extend
this line to the vertex of this
rectangle awesome now consider these two
triangles this angle is the same for
both these triangles and also since both
of these lines are parallel this angle
is also the same for both of them and
hence both these triangles are s similar
therefore this side which is 2 over this
side which is 1.5 equals this side which
is y + 2 over this side which is 3 cross
multiply to get this this becomes 6 over
1.5 or 4 = y + 2 or Y = 2 woohoo now is
the time for our final answer drums
rolling in and and it is 1 + 2 + 2 or 5
which is exactly the same as we
predicted at the beginning of this video
when we looked at this problem
visually isn't this cool if you liked
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